Question

In: Statistics and Probability

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly....

The commercial for the new Meat Man Barbecue claims that it takes 10 minutes for assembly. A consumer advocate thinks that the assembly time is lower than 10 minutes. The advocate surveyed 12 randomly selected people who purchased the Meat Man Barbecue and found that their average time was 9.5 minutes. The standard deviation for this survey group was 2.9 minutes. What can be concluded at the the α α = 0.10 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H 0 : H 0 : H 1 : H 1 : The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is α α Based on this, we should the null hypothesis. Thus, the final conclusion is that ... The data suggest the populaton mean is significantly lower than 10 at α α = 0.10, so there is statistically significant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 10. The data suggest the population mean is not significantly lower than 10 at α α = 0.10, so there is nstatistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is equal to 10. The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly lower than 10 at α α = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 10.

Solutions

Expert Solution

a) 1 sample z test for sample mean

b)

null hypothesis:Ho μ = 10
Alternate Hypothesis:Ha μ < 10

c)

population mean μ= 10
sample mean 'x̄= 9.500
sample size    n= 12.00
std deviation σ= 2.900
std error ='σx=σ/√n= 0.8372
test stat z = '(x̄-μ)*√n/σ=   -0.597

d)

p value        = 0.2752

p value greater than alpha

we should not reject the null hypothesis

The data suggest that the population mean amount of time to assemble the Meat Man barbecue is not significantly lower than 10 at α = 0.10, so there is statistically insignificant evidence to conclude that the population mean amount of time to assemble the Meat Man barbecue is lower than 10.


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